The General Linear Model 12.2

Front 1

It is important at this point to recognize that a single general model can be used for multiple regression models in which a response is related to a set of quantitative independent variables, and for models that relate y to a set of qualitative inde- pendent variables. This model, called the _____________, has the form
y = b0 + b1x1 + b2x2 + . . . + bkxk + e

Back 1

general linear model

Front 2

For _____________ models, the xs represent quantitative independent variables (such as weight or amount of water), independent variables raised to powers, and cross-product terms involving the independent variables.

Back 2

multiple regression

Front 3

When y is related to a set of ____________ independent variables the xs of the general linear model represent dummy variables (coded 0 and 1) or products of dummy variables. We discussed how to use dummy variables for representing y in terms of a _________ qualitative variable in Section 12.1; the same approach can be used to relate y to more than one qualitative independent variable.

Back 3

qualitative, single

Front 4

The general linear model can also be used for the case in which _____ is related to both qualitative and quantitative independent variables.

Back 4

y

Front 5

The word “linear’’ in the general linear model refers to how the bs are entered in the model, not to how the independent variables appear in the model. A general linear model is linear (used in the usual algebraic sense) in the _______. That is, the bs do not appear as exponents or as the argument of a nonlinear function.

Back 5

bs

Front 6

____________ is a special case of a general linear model.

Back 6

multiple regression